We are studying the structures of polypeptide-like polymer chains created by a random walk procedure. A polypeptide backbone is created that retains the geometric features of a peptide (bond lengths, bond angles, and torsional angles) and adheres to the constraints imposed by a van der Waals repulsive interaction. Chains that are not compact are eliminated as well. In this way, we create an ensemble of polypeptide chains that contain the most basic features of proteins. From these simulations, we have learned that, as the chain becomes increasingly compact, it is more likely to contain secondary structure. This is consistent with the findings of Dill and colleagues using cubic lattice models of protein structure. Unfortunately, the chains must be approximately 20-30% more compact than native protein structures to achieve a secondary structure content compatible with known protein structures. Moreover, only alpha-helices are seen under these conditions. While beta-strands are common, beta-sheets are not seen. Perhaps sheet formation is an artifact of the cubic lattice. This suggestion is supported by the fact that beta-sheets are not observed for compact chains generated on a tetrahedral lattice. We were concerned that our initial work explored only polyalanine models of protein sequences. Recently, we have overcome this limitation and are now studying chains with a variety of side chains. Preliminary studies support our earlier work with polyalanine chains. Perhaps hydrogen bonds are important to the stability of secondary structure, especially beta-sheets. This is consistent with Pauling's early observations, but it is difficult to understand why a hydrogen bond within a protein should be stronger than a peptide-water hydrogen bond. Polymer simulations allow us to ask what strength must be assigned to a hydrogen bond to reproduce the observed secondary structure content of proteins at a density that is consistent with proteins of known structure. These studies are underway. Current molecular mechanics force fields provide a detailed view of molecular motions. Unfortunately, their complexity, coupled with current limits on computer speed, prevent computational chemists from simulating protein processes that take longer than a nanosecond. The time required to simulate a molecular motion relates to the square of the number of atoms and the maximum size of a stable time step during numerical integration of the equations of motion. To speed up a simulation, one must find a faster computer or decrease the number of effective atoms and increase the stable time-step size. We are building an intermediate-resolution force field that approximates amino acids by a sphere for the backbone and a sphere for the side chain. Aromatic residues require two (or three) spheres for each side chain. A backbone potential that mimics the behavior of more realistic allatom backbone representations has been developed. We are currently exploring a hydrogen-bonding potential (a challenge when there are no explicit amide nitrogens or carbonyl oxygens) and an implicit solvent-interaction term that avoids the need for the explicit inclusion of water molecules in the simulation. This remains an ambitious program, but preliminary calculations suggest that SPEEDY, a Simplified Potential for Energy Evaluation and DYnamics, runs approximately 100 times faster than current molecular mechanics packages, such as AMBER.